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Chapter 5: Q 87. (page 299)

Solve the equation.
$\log_{3} (x) = 2$

Short Answer

Expert verified

The solution to the equation, $\log_{3} (x) = 2$ is, $x = 9$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $\log_{3} (x) = 2$ .

02

Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

03

Step 3. Finding Solution

The given equation is $\log_{3} (x) = 2$ .

Use rule of change from logarithm to exponents:

$\log_{3} (x) = 2 x = 3^{2} x = 9$

The solution to the given equationis, $x = 9$ .

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Most popular questions from this chapter

Solve the equation ${(\frac{1}{4})}^{x} = \frac{1}{64}$

and verify your results using a graphing utility.

solve each equation. Verify your results using a graphing utility.

$e^{x} = e^{3 x + 8}$

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{3 x + 4}{2 x - 3}$

Use the graph of $y = f (x)$ given in the Problem $43$ to evaluate the following:

(a) $f (- 1)$

(b) $f (1)$

(c) $f^{- 1} (1)$

(d) $f^{- 1} (2)$

Evaluate each expression using the graphs of $y = f (x)$ and $y = g (x)$ shown in the figure.

(a) $(g \circ f) (- 1)$ (b) $(g \circ f) (0)$ (c) $(f \circ g) (- 1)$ (d) $(f \circ g) (4)$ .

See all solutions

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